A multiple of the identity matrix of static size. More...

#include <dune/istl/scaledidmatrix.hh>

Public Types
enum	{ rows = n , cols = n }
	export size More...

typedef K	field_type
	export the type representing the field More...

typedef K	block_type
	export the type representing the components More...

typedef std::size_t	size_type
	The type used for the index access and size operations. More...

typedef DiagonalRowVector< K, n >	row_type
	Each row is implemented by a field vector. More...

typedef row_type	reference

typedef DiagonalRowVectorConst< K, n >	const_row_type

typedef const_row_type	const_reference

typedef ContainerWrapperIterator< const WrapperType, reference, reference >	Iterator
	Iterator class for sequential access. More...

typedef Iterator	iterator
	typedef for stl compliant access More...

typedef Iterator	RowIterator
	rename the iterators for easier access More...

typedef row_type::Iterator	ColIterator
	rename the iterators for easier access More...

typedef ContainerWrapperIterator< const WrapperType, const_reference, const_reference >	ConstIterator
	Iterator class for sequential access. More...

typedef ConstIterator	const_iterator
	typedef for stl compliant access More...

typedef ConstIterator	ConstRowIterator
	rename the iterators for easier access More...

typedef const_row_type::ConstIterator	ConstColIterator
	rename the iterators for easier access More...

Public Member Functions
	ScaledIdentityMatrix ()
	Default constructor. More...

	ScaledIdentityMatrix (const K &k)
	Constructor initializing the whole matrix with a scalar. More...

ScaledIdentityMatrix &	operator= (const K &k)

bool	identical (const ScaledIdentityMatrix< K, n > &other) const

Iterator	begin ()
	begin iterator More...

Iterator	end ()
	end iterator More...

Iterator	beforeEnd ()

Iterator	beforeBegin ()

ConstIterator	begin () const
	begin iterator More...

ConstIterator	end () const
	end iterator More...

ConstIterator	beforeEnd () const

ConstIterator	beforeBegin () const

ScaledIdentityMatrix &	operator+= (const ScaledIdentityMatrix &y)
	vector space addition More...

ScaledIdentityMatrix &	operator-= (const ScaledIdentityMatrix &y)
	vector space subtraction More...

ScaledIdentityMatrix &	operator+= (const K &k)
	addition to the diagonal More...

ScaledIdentityMatrix &	operator-= (const K &k)
	subtraction from the diagonal More...

ScaledIdentityMatrix &	operator*= (const K &k)
	vector space multiplication with scalar More...

ScaledIdentityMatrix &	operator/= (const K &k)
	vector space division by scalar More...

bool	operator== (const ScaledIdentityMatrix &other) const
	comparison operator More...

bool	operator!= (const ScaledIdentityMatrix &other) const
	incomparison operator More...

template<class X , class Y >
void	mv (const X &x, Y &y) const
	y = A x More...

template<class X , class Y >
void	mtv (const X &x, Y &y) const
	y = A^T x More...

template<class X , class Y >
void	umv (const X &x, Y &y) const
	y += A x More...

template<class X , class Y >
void	umtv (const X &x, Y &y) const
	y += A^T x More...

template<class X , class Y >
void	umhv (const X &x, Y &y) const
	y += A^H x More...

template<class X , class Y >
void	mmv (const X &x, Y &y) const
	y -= A x More...

template<class X , class Y >
void	mmtv (const X &x, Y &y) const
	y -= A^T x More...

template<class X , class Y >
void	mmhv (const X &x, Y &y) const
	y -= A^H x More...

template<class X , class Y >
void	usmv (const K &alpha, const X &x, Y &y) const
	y += alpha A x More...

template<class X , class Y >
void	usmtv (const K &alpha, const X &x, Y &y) const
	y += alpha A^T x More...

template<class X , class Y >
void	usmhv (const K &alpha, const X &x, Y &y) const
	y += alpha A^H x More...

FieldTraits< field_type >::real_type	frobenius_norm () const
	frobenius norm: sqrt(sum over squared values of entries) More...

FieldTraits< field_type >::real_type	frobenius_norm2 () const
	square of frobenius norm, need for block recursion More...

FieldTraits< field_type >::real_type	infinity_norm () const
	infinity norm (row sum norm, how to generalize for blocks?) More...

FieldTraits< field_type >::real_type	infinity_norm_real () const
	simplified infinity norm (uses Manhattan norm for complex values) More...

template<class V >
void	solve (V &x, const V &b) const
	Solve system A x = b. More...

void	invert ()
	Compute inverse. More...

K	determinant () const
	calculates the determinant of this matrix More...

size_type	N () const
	number of blocks in row direction More...

size_type	M () const
	number of blocks in column direction More...

bool	exists (size_type i, size_type j) const
	return true when (i,j) is in pattern More...

reference	operator[] (size_type i)
	Return reference object as row replacement. More...

const_reference	operator[] (size_type i) const
	Return const_reference object as row replacement. More...

const K &	diagonal (size_type) const
	Get const reference to diagonal entry. More...

K &	diagonal (size_type)
	Get reference to diagonal entry. More...

const K &	scalar () const
	Get const reference to the scalar diagonal value. More...

K &	scalar ()
	Get reference to the scalar diagonal value. More...

Static Public Attributes
static constexpr std::size_t	blocklevel = 1
	We are at the leaf of the block recursion. More...

Detailed Description

template<class K, int n>
class Dune::ScaledIdentityMatrix< K, n >

A multiple of the identity matrix of static size.

Member Typedef Documentation

◆ block_type

template<class K , int n>

typedef K Dune::ScaledIdentityMatrix< K, n >::block_type

export the type representing the components

◆ ColIterator

template<class K , int n>

typedef row_type::Iterator Dune::ScaledIdentityMatrix< K, n >::ColIterator

rename the iterators for easier access

◆ const_iterator

template<class K , int n>

typedef ConstIterator Dune::ScaledIdentityMatrix< K, n >::const_iterator

typedef for stl compliant access

◆ const_reference

template<class K , int n>

typedef const_row_type Dune::ScaledIdentityMatrix< K, n >::const_reference

◆ const_row_type

template<class K , int n>

typedef DiagonalRowVectorConst<K,n> Dune::ScaledIdentityMatrix< K, n >::const_row_type

◆ ConstColIterator

template<class K , int n>

typedef const_row_type::ConstIterator Dune::ScaledIdentityMatrix< K, n >::ConstColIterator

rename the iterators for easier access

◆ ConstIterator

template<class K , int n>

typedef ContainerWrapperIterator<const WrapperType, const_reference, const_reference> Dune::ScaledIdentityMatrix< K, n >::ConstIterator

Iterator class for sequential access.

◆ ConstRowIterator

template<class K , int n>

typedef ConstIterator Dune::ScaledIdentityMatrix< K, n >::ConstRowIterator

rename the iterators for easier access

◆ field_type

template<class K , int n>

typedef K Dune::ScaledIdentityMatrix< K, n >::field_type

export the type representing the field

◆ Iterator

template<class K , int n>

typedef ContainerWrapperIterator<const WrapperType, reference, reference> Dune::ScaledIdentityMatrix< K, n >::Iterator

Iterator class for sequential access.

◆ iterator

template<class K , int n>

typedef Iterator Dune::ScaledIdentityMatrix< K, n >::iterator

typedef for stl compliant access

◆ reference

template<class K , int n>

typedef row_type Dune::ScaledIdentityMatrix< K, n >::reference

◆ row_type

template<class K , int n>

typedef DiagonalRowVector<K,n> Dune::ScaledIdentityMatrix< K, n >::row_type

Each row is implemented by a field vector.

◆ RowIterator

template<class K , int n>

typedef Iterator Dune::ScaledIdentityMatrix< K, n >::RowIterator

rename the iterators for easier access

◆ size_type

template<class K , int n>

typedef std::size_t Dune::ScaledIdentityMatrix< K, n >::size_type

The type used for the index access and size operations.

Member Enumeration Documentation

◆ anonymous enum

template<class K , int n>

anonymous enum

export size

Enumerator
rows	The number of rows.
cols	The number of columns.

Constructor & Destructor Documentation

◆ ScaledIdentityMatrix() [1/2]

template<class K , int n>

Dune::ScaledIdentityMatrix< K, n >::ScaledIdentityMatrix ( )

inline

Default constructor.

◆ ScaledIdentityMatrix() [2/2]

template<class K , int n>

Dune::ScaledIdentityMatrix< K, n >::ScaledIdentityMatrix ( const K & k )

inline

Constructor initializing the whole matrix with a scalar.

Member Function Documentation

◆ beforeBegin() [1/2]

template<class K , int n>

Iterator Dune::ScaledIdentityMatrix< K, n >::beforeBegin ( )

inline

Returns: an iterator that is positioned before the first row of the matrix.

◆ beforeBegin() [2/2]

template<class K , int n>

ConstIterator Dune::ScaledIdentityMatrix< K, n >::beforeBegin ( ) const

inline

Returns: an iterator that is positioned before the first row of the matrix.

◆ beforeEnd() [1/2]

template<class K , int n>

Iterator Dune::ScaledIdentityMatrix< K, n >::beforeEnd ( )

inline

Returns: an iterator that is positioned before the end iterator of the rows, i.e. at the last row.

◆ beforeEnd() [2/2]

template<class K , int n>

ConstIterator Dune::ScaledIdentityMatrix< K, n >::beforeEnd ( ) const

inline

Returns: an iterator that is positioned before the end iterator of the rows. i.e. at the last row.

◆ begin() [1/2]

template<class K , int n>

Iterator Dune::ScaledIdentityMatrix< K, n >::begin ( )

inline

begin iterator

◆ begin() [2/2]

template<class K , int n>

ConstIterator Dune::ScaledIdentityMatrix< K, n >::begin ( ) const

inline

begin iterator

◆ determinant()

template<class K , int n>

K Dune::ScaledIdentityMatrix< K, n >::determinant ( ) const

inline

calculates the determinant of this matrix

◆ diagonal() [1/2]

template<class K , int n>

K & Dune::ScaledIdentityMatrix< K, n >::diagonal ( size_type )

inline

Get reference to diagonal entry.

◆ diagonal() [2/2]

template<class K , int n>

const K & Dune::ScaledIdentityMatrix< K, n >::diagonal ( size_type ) const

inline

Get const reference to diagonal entry.

◆ end() [1/2]

template<class K , int n>

Iterator Dune::ScaledIdentityMatrix< K, n >::end ( )

inline

end iterator

◆ end() [2/2]

template<class K , int n>

ConstIterator Dune::ScaledIdentityMatrix< K, n >::end ( ) const

inline

end iterator

◆ exists()

template<class K , int n>

bool Dune::ScaledIdentityMatrix< K, n >::exists	(	size_type	i,
		size_type	j
	)		const

inline

return true when (i,j) is in pattern

◆ frobenius_norm()

template<class K , int n>

FieldTraits< field_type >::real_type Dune::ScaledIdentityMatrix< K, n >::frobenius_norm ( ) const

inline

frobenius norm: sqrt(sum over squared values of entries)

◆ frobenius_norm2()

template<class K , int n>

FieldTraits< field_type >::real_type Dune::ScaledIdentityMatrix< K, n >::frobenius_norm2 ( ) const

inline

square of frobenius norm, need for block recursion

◆ identical()

template<class K , int n>

bool Dune::ScaledIdentityMatrix< K, n >::identical ( const ScaledIdentityMatrix< K, n > & other ) const

inline

◆ infinity_norm()

template<class K , int n>

FieldTraits< field_type >::real_type Dune::ScaledIdentityMatrix< K, n >::infinity_norm ( ) const

inline

infinity norm (row sum norm, how to generalize for blocks?)

◆ infinity_norm_real()

template<class K , int n>

FieldTraits< field_type >::real_type Dune::ScaledIdentityMatrix< K, n >::infinity_norm_real ( ) const

inline

simplified infinity norm (uses Manhattan norm for complex values)

◆ invert()

template<class K , int n>

void Dune::ScaledIdentityMatrix< K, n >::invert ( )

inline

Compute inverse.

◆ M()

template<class K , int n>

size_type Dune::ScaledIdentityMatrix< K, n >::M ( ) const

inline

number of blocks in column direction

◆ mmhv()

template<class K , int n>

template<class X , class Y >

void Dune::ScaledIdentityMatrix< K, n >::mmhv	(	const X &	x,
		Y &	y
	)		const

inline

y -= A^H x

◆ mmtv()

template<class K , int n>

template<class X , class Y >

void Dune::ScaledIdentityMatrix< K, n >::mmtv	(	const X &	x,
		Y &	y
	)		const

inline

y -= A^T x

◆ mmv()

template<class K , int n>

template<class X , class Y >

void Dune::ScaledIdentityMatrix< K, n >::mmv	(	const X &	x,
		Y &	y
	)		const

inline

y -= A x

◆ mtv()

template<class K , int n>

template<class X , class Y >

void Dune::ScaledIdentityMatrix< K, n >::mtv	(	const X &	x,
		Y &	y
	)		const

inline

y = A^T x

◆ mv()

template<class K , int n>

template<class X , class Y >

void Dune::ScaledIdentityMatrix< K, n >::mv	(	const X &	x,
		Y &	y
	)		const

inline

y = A x

◆ N()

template<class K , int n>

size_type Dune::ScaledIdentityMatrix< K, n >::N ( ) const

inline

number of blocks in row direction

◆ operator!=()

template<class K , int n>

bool Dune::ScaledIdentityMatrix< K, n >::operator!= ( const ScaledIdentityMatrix< K, n > & other ) const

inline

incomparison operator

◆ operator*=()

template<class K , int n>

ScaledIdentityMatrix & Dune::ScaledIdentityMatrix< K, n >::operator*= ( const K & k )

inline

vector space multiplication with scalar

◆ operator+=() [1/2]

template<class K , int n>

ScaledIdentityMatrix & Dune::ScaledIdentityMatrix< K, n >::operator+= ( const K & k )

inline

addition to the diagonal

◆ operator+=() [2/2]

template<class K , int n>

ScaledIdentityMatrix & Dune::ScaledIdentityMatrix< K, n >::operator+= ( const ScaledIdentityMatrix< K, n > & y )

inline

vector space addition

◆ operator-=() [1/2]

template<class K , int n>

ScaledIdentityMatrix & Dune::ScaledIdentityMatrix< K, n >::operator-= ( const K & k )

inline

subtraction from the diagonal

◆ operator-=() [2/2]

template<class K , int n>

ScaledIdentityMatrix & Dune::ScaledIdentityMatrix< K, n >::operator-= ( const ScaledIdentityMatrix< K, n > & y )

inline

vector space subtraction

◆ operator/=()

template<class K , int n>

ScaledIdentityMatrix & Dune::ScaledIdentityMatrix< K, n >::operator/= ( const K & k )

inline

vector space division by scalar

◆ operator=()

template<class K , int n>

ScaledIdentityMatrix & Dune::ScaledIdentityMatrix< K, n >::operator= ( const K & k )

inline

◆ operator==()

template<class K , int n>

bool Dune::ScaledIdentityMatrix< K, n >::operator== ( const ScaledIdentityMatrix< K, n > & other ) const

inline

comparison operator

◆ operator[]() [1/2]

template<class K , int n>

reference Dune::ScaledIdentityMatrix< K, n >::operator[] ( size_type i )

inline

Return reference object as row replacement.

◆ operator[]() [2/2]

template<class K , int n>

const_reference Dune::ScaledIdentityMatrix< K, n >::operator[] ( size_type i ) const

inline

Return const_reference object as row replacement.

◆ scalar() [1/2]

template<class K , int n>

K & Dune::ScaledIdentityMatrix< K, n >::scalar ( )

inline

Get reference to the scalar diagonal value.

◆ scalar() [2/2]

template<class K , int n>

const K & Dune::ScaledIdentityMatrix< K, n >::scalar ( ) const

inline

Get const reference to the scalar diagonal value.

◆ solve()

template<class K , int n>

template<class V >

void Dune::ScaledIdentityMatrix< K, n >::solve	(	V &	x,
		const V &	b
	)		const

inline

Solve system A x = b.

◆ umhv()

template<class K , int n>

template<class X , class Y >

void Dune::ScaledIdentityMatrix< K, n >::umhv	(	const X &	x,
		Y &	y
	)		const

inline

y += A^H x

◆ umtv()

template<class K , int n>

template<class X , class Y >

void Dune::ScaledIdentityMatrix< K, n >::umtv	(	const X &	x,
		Y &	y
	)		const

inline

y += A^T x

◆ umv()

template<class K , int n>

template<class X , class Y >

void Dune::ScaledIdentityMatrix< K, n >::umv	(	const X &	x,
		Y &	y
	)		const

inline

y += A x

◆ usmhv()

template<class K , int n>

template<class X , class Y >

void Dune::ScaledIdentityMatrix< K, n >::usmhv	(	const K &	alpha,
		const X &	x,
		Y &	y
	)		const

inline

y += alpha A^H x

◆ usmtv()

template<class K , int n>

template<class X , class Y >

void Dune::ScaledIdentityMatrix< K, n >::usmtv	(	const K &	alpha,
		const X &	x,
		Y &	y
	)		const

inline

y += alpha A^T x

◆ usmv()

template<class K , int n>

template<class X , class Y >

void Dune::ScaledIdentityMatrix< K, n >::usmv	(	const K &	alpha,
		const X &	x,
		Y &	y
	)		const

inline

y += alpha A x

Member Data Documentation

◆ blocklevel

template<class K , int n>

constexpr std::size_t Dune::ScaledIdentityMatrix< K, n >::blocklevel = 1

staticconstexpr

We are at the leaf of the block recursion.

The documentation for this class was generated from the following file:

scaledidmatrix.hh

Public Types

Public Member Functions

Static Public Attributes

Detailed Description

Member Typedef Documentation

◆ block_type

◆ ColIterator

◆ const_iterator

◆ const_reference

◆ const_row_type

◆ ConstColIterator

◆ ConstIterator

◆ ConstRowIterator

◆ field_type

◆ Iterator

◆ iterator

◆ reference

◆ row_type

◆ RowIterator

◆ size_type

Member Enumeration Documentation

◆ anonymous enum

Constructor & Destructor Documentation

◆ ScaledIdentityMatrix() [1/2]

◆ ScaledIdentityMatrix() [2/2]

Member Function Documentation

◆ beforeBegin() [1/2]

◆ beforeBegin() [2/2]

◆ beforeEnd() [1/2]

◆ beforeEnd() [2/2]

◆ begin() [1/2]

◆ begin() [2/2]

◆ determinant()

◆ diagonal() [1/2]

◆ diagonal() [2/2]

◆ end() [1/2]

◆ end() [2/2]

◆ exists()

◆ frobenius_norm()

◆ frobenius_norm2()

◆ identical()

◆ infinity_norm()

◆ infinity_norm_real()

◆ invert()

◆ M()

◆ mmhv()

◆ mmtv()

◆ mmv()

◆ mtv()

◆ mv()

◆ N()

◆ operator!=()

◆ operator*=()

◆ operator+=() [1/2]

◆ operator+=() [2/2]

◆ operator-=() [1/2]

◆ operator-=() [2/2]

◆ operator/=()

◆ operator=()

◆ operator==()

◆ operator[]() [1/2]

◆ operator[]() [2/2]

◆ scalar() [1/2]

◆ scalar() [2/2]

◆ solve()

◆ umhv()

◆ umtv()

◆ umv()

◆ usmhv()

◆ usmtv()

◆ usmv()

Member Data Documentation

◆ blocklevel